In　this　paper,　we　will　study　solutions　of　the　(2+1)-dimensional　extended　Bogoyavlenskii-Kadomtsev-Petviashvili　(eBKP)　equation　which　describes　nonlinear　wave　propagation　in　superfluids,　plasma　physics　and　fluid　dynamics.　We　successfully　apply　the　generalized　Kudryashov　technique　to　obtain　many　solutions　of　the　eBKP　equation.　These　solutions　include　not　only　rational　fraction　solution,　tanh　solutions,　coth　solutions,　trigonometric　periodic　solutions,　but　also　some　new　elliptic　function　solutions　which　are　firstly　obtained　in　our　paper.　Some　solutions　have　linear　tails　which　may　explain　some　physical　phenomena.　The　technique　is　effective,　easily　applicable,　and　reliable　in　solving　such　nonlinear　problems.　Moreover,　we　give　some　3D　and　2D　graphics　to　describe　the　properties　of　solutions　and　analyze　the　effects　of　linear　tails.